Literal Equations and Formulas

Key Concepts

• Rewrite literal equations
• Use literal equations to solve problems
• Rewrite a formula
• Apply formulas

Literal equation 

An equation that states the relationship between two or more quantities using variables is called a literal equation. 

Example: Frame a literal equation for the perimeter of a rectangle. 

The perimeter of a rectangle = Sum of all sides 

= Length + Width + Length + Width 

Let P be the perimeter, l be the length and w be the width of the rectangle  

P = 2 × (l+ w) 

Formula 

An equation that states the relationship between one quantity and one or more quantities is called a formula. 

We use formulas for finding the unknown values like perimeter and area. 

1. Formula for perimeter of square 

P = 4 × Side 

2. Formula for perimeter of rectangle 

P = 2 (length + width) 

3. Formula for area of square 

A = Side × Side 

4. Formula for area of rectangle 

A = length × width 

Rewriting literal equations 

Use properties of equality to solve literal equations for a variable just as you do linear equations. 

Example:  

If the side of the square is s, then perimeter P = s + s + s + s 

P = 4 × s 

If we are given the perimeter of a square, to find the length of each side, we need to divide the formula of perimeter of a square by “4”. 

P/4 = 4×s/4

⇒ s = P/4

Rewriting a formula 

We can rewrite a formula to find the unknown values. Then we get the value of one quantity in terms of another quantity. 

Example: Write the formula for calculating the length of a rectangle if the perimeter and the width are given. 

Sol: The formula for the perimeter of a rectangular farm is   P = 2(l+ w) 

P = 2l+ 2w 

P – 2w = 2l + 2w – 2w 

P – 2w/2 = 2l/2

l= P−2w/2

∴ The perimeter formula in terms of l is l = P−2w/2

Apply formula 

We can use the formulas to rewrite/reframe them and solve problems. 

Example: The high temperature on a given winter day is 25° C. What is the temperature in °F? 

Rewrite the formula to find the Fahrenheit temperature that is equal to 25° C 

C = 5/9(F – 32) 

9/5 . C = 9/5 . 5/9(F – 32) 

9/5C = F – 32 

9/5C + 32 = F – 32 + 32 

9/5C + 32 = F 

Use the formula to find the Fahrenheit temperature equivalent to 25° C 

9/5C + 32 = F 

9/5(25) + 32 = F 

45 + 32 = F 

F = 77°  

Exercise

• Solve 5x-4 = 4x
• The triangle shown is isosceles. Find the length of the third side of the triangle.

• Solve the equation – 3(8+3h) = 5h+4
• Find the missing value in – 2(2x- ?) + 1 = 17-4x
• Is the equation – 4(3-2x) = -12-8x an identity?

So, the high temperature on a given winter day is 77° F. 

Concept Map

If an equation has pronumerals on both sides, collect the like terms to one side by adding or subtracting terms. 

Example: 4x + 7 = 2(2x + 1) + 5 

4x + 7 = 4x + 2 + 5 

4x + 7 = 4x + 7 

7 = 7 

What have we learned

• If an equation has pronumerals on both sides, collect the like terms to one side by adding or subtracting terms